Beverage service in fast food restaurants, concession stands and other locations where beverages are dispensed commonly utilize containers having lids formed of thin plastic material. It is desirable to have a means for opening a portion of such lids so that the beverage can be consumed from the container while at the same time a major portion of the lid remains intact on the container to prevent spillage. Prior art lids of this type have included segments defined by predetermined score lines which were intended to rupture so that the segment could be removed. It was found however that many times the material of the lid would not rupture along the score lines provided, but rather would tear in erratic fashion into the material adjacent the score lines. It has now been determined in accordance with this invention that a score line configuration can be devised which will permit reliable rupturing along an intended path and result in complete freeing of a lid segment.